78,088 research outputs found

### On representations of quantum groups $U_{q}(f_{m}(K,H))$

We construct families of irreducible representations for a class of quantum
groups $U_{q}(f_{m}(K,H)$. First, we realize these quantum groups as Hyperbolic
algebras. Such a realization yields natural families of irreducible weight
representations for $U_{q}(f_{m}(K,H))$. Second, we study the relationship
between $U_{q}(f_{m}(K,H))$ and $U_{q}(f_{m}(K))$. As a result, any finite
dimensional weight representation of $U_{q}(f_{m}(K,H))$ is proved to be
completely reducible. Finally, we study the Whittaker model for the center of
$U_{q}(f_{m}(K,H))$, and a classification of all irreducible Whittaker
representations of $U_{q}(f_{m}(K,H))$ is obtained.Comment: Some minor modifications to the first versio

### Acoustic Prism for Continuous Beam Steering Based on Piezoelectric Metamaterial

This paper investigates an acoustic prism for continuous acoustic beam
steering by a simple frequency sweep. This idea takes advantages of acoustic
wave velocity shifting in metamaterials in the vicinity of local resonance. We
apply this concept into the piezoelectric metamaterial consisting of host
medium and piezoelectric LC shunt. Theoretical modeling and FEM simulations are
carried out. It is shown that the phase velocity of acoustic wave changes
dramatically in the vicinity of local resonance. The directions of acoustic
wave can be adjusted continuously between 2 to 16 degrees by a simple sweep of
the excitation frequency. Such an electro-mechanical coupling system has a
feature of adjusting local resonance without altering the mechanical part of
the system.Comment: 11 pages, 11 figure

### Stability of the sum of two solitary waves for (gDNLS) in the energy space

In this paper, we continue the study in \cite{MiaoTX:DNLS:Stab}. We use the
perturbation argument, modulational analysis and the energy argument in
\cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS} to show the stability of the sum
of two solitary waves with weak interactions for the generalized derivative
Schr\"{o}dinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the
Galilean transformation invariance, the pseudo-conformal invariance and the
gauge transformation invariance, and the case $\sigma>1$ we considered
corresponds to the $L^2$-supercritical case.Comment: 41page

### Detecting the Major Charge-Carrier Scattering Mechanism in Graphene Antidot Lattices

Charge carrier scattering is critical to the electrical properties of
two-dimensional materials such as graphene, transition metal dichalcogenide
monolayers, black phosphorene, and tellurene. Beyond pristine two-dimensional
materials, further tailored properties can be achieved by nanoporous patterns
such as nano- or atomic-scale pores (antidots) across the material. As one
example, structure-dependent electrical/optical properties for graphene antidot
lattices (GALs) have been studied in recent years. However, detailed charge
carrier scattering mechanism is still not fully understood, which hinders the
future improvement and potential applications of such metamaterials. In this
paper, the energy sensitivity of charge-carrier scattering and thus the
dominant scattering mechanisms are revealed for GALs by analyzing the maximum
Seebeck coefficient with a tuned gate voltage and thus shifted Fermi levels. It
shows that the scattering from pore-edge-trapped charges is dominant,
especially at elevated temperatures. For thermoelectric interests, the
gate-voltage-dependent power factor of different GAL samples are measured as
high as 509 at 400 K for a GAL with the square pattern. Such a high power
factor is improved by more than one order of magnitude from the values for the
state-of-the-art bulk thermoelectric materials. With their high thermal
conductivities and power factors, these GALs can be well suitable for "active
coolers" within electronic devices, where heat generated at the hot spot can be
removed with both passive heat conduction and active Peltier cooling

### The Cosmological Constant as a Function of Extrinsic Curvature and Spatial Curvature

In this paper we suppose that the cosmological constant will change when the
universe expends. For a general consideration, the cosmological constant is
assumed to be a function of scale factor and Hubble constant. According to the
ADM formulation, to the FRW metric, the extrinsic curvature $I$ equals
$-6H^{2}$ and spatial curvature $R$ equals $6k/a^{2}$. Therefore we suppose
cosmological constant is a function of extrinsic curvature and spatial
curvature. We investigate the cosmological evolution of FRW universe in these
models. At last we investigate two particular models which could fit the
observation data about dark energy well. Actually a changeless cosmological
constant is not essential. If when the universe expands, the cosmological
constant changes slowly and gradually flows to a constant, the observation data
about dark energy could also be fitted well by this kind of theory.Comment: 8 pages, 4 figure

### Fermion correction to the mass of the scalar glueball in QCD sum rule

Contributions of fermions to the mass of the scalar glueball $0^{++}$ are
calculated at two-loop level in the framework of QCD sum rules. It obviously
changes the coefficients in the operator product expansion (OPE) and shifts the
mass of glueball.Comment: 5 pages, 2 figure

### Parallel in time algorithm with spectral-subdomain enhancement for Volterra integral equations

This paper proposes a parallel in time (called also time parareal) method to
solve Volterra integral equations of the second kind. The parallel in time
approach follows the same spirit as the domain decomposition that consists of
breaking the domain of computation into subdomains and solving iteratively the
sub-problems in a parallel way. To obtain high order of accuracy, a spectral
collocation accuracy enhancement in subdomains will be employed. Our main
contributions in this work are two folds: (i) a time parareal method is
designed for the integral equations, which to our knowledge is the first of its
kind. The new method is an iterative process combining a coarse prediction in
the whole domain with fine corrections in subdomains by using spectral
approximation, leading to an algorithm of very high accuracy; (ii) a rigorous
convergence analysis of the overall method is provided. The numerical
experiment confirms that the overall computational cost is considerably reduced
while the desired spectral rate of convergence can be obtained

### On the Performance of Sparse Recovery via L_p-minimization (0<=p <=1)

It is known that a high-dimensional sparse vector x* in R^n can be recovered
from low-dimensional measurements y= A^{m*n} x* (m<n) . In this paper, we
investigate the recovering ability of l_p-minimization (0<=p<=1) as p varies,
where l_p-minimization returns a vector with the least l_p ``norm'' among all
the vectors x satisfying Ax=y. Besides analyzing the performance of strong
recovery where l_p-minimization needs to recover all the sparse vectors up to
certain sparsity, we also for the first time analyze the performance of
``weak'' recovery of l_p-minimization (0<=p<1) where the aim is to recover all
the sparse vectors on one support with fixed sign pattern. When m/n goes to 1,
we provide sharp thresholds of the sparsity ratio that differentiates the
success and failure via l_p-minimization. For strong recovery, the threshold
strictly decreases from 0.5 to 0.239 as p increases from 0 to 1. Surprisingly,
for weak recovery, the threshold is 2/3 for all p in [0,1), while the threshold
is 1 for l_1-minimization. We also explicitly demonstrate that l_p-minimization
(p<1) can return a denser solution than l_1-minimization. For any m/n<1, we
provide bounds of sparsity ratio for strong recovery and weak recovery
respectively below which l_p-minimization succeeds with overwhelming
probability. Our bound of strong recovery improves on the existing bounds when
m/n is large. Regarding the recovery threshold, l_p-minimization has a higher
threshold with smaller p for strong recovery; the threshold is the same for all
p for sectional recovery; and l_1-minimization can outperform l_p-minimization
for weak recovery. These are in contrast to traditional wisdom that
l_p-minimization has better sparse recovery ability than l_1-minimization since
it is closer to l_0-minimization. We provide an intuitive explanation to our
findings and use numerical examples to illustrate the theoretical predictions

### An Improved Error Term for Tur$\acute{\rm a}$n Number of Expanded Non-degenerate 2-graphs

For a 2-graph $F$, let $H_F^{(r)}$ be the $r$-graph obtained from $F$ by
enlarging each edge with a new set of $r-2$ vertices. We show that if
$\chi(F)=\ell>r \geq 2$, then ${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)+ \Theta(
{\rm biex}(n,F)n^{r-2}),$ where $t_r (n,\ell-1)$ is the number of edges of an
$n$-vertex complete balanced $\ell-1$ partite $r$-graph and ${\rm biex}(n,F)$
is the extremal number of the decomposition family of $F$. Since ${\rm
biex}(n,F)=O(n^{2-\gamma})$ for some $\gamma>0$, this improves on the bound
${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)+ o(n^r)$ by Mubayi (2016). Furthermore,
our result implies that ${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)$ when $F$ is
edge-critical, which is an extension of the result of Pikhurko (2013)

### Spin alignment of vector mesons in unpolarized hadron-hadron collisions at high energies

We argue that spin alignment of the vector mesons observed in unpolarized
hadron-hadron collisions is closely related to the single spin left-right
asymmetry observed in transversely polarized hadron-hadron collisions. We
present the numerical results obtained from the type of spin-correlation
imposed by the existence of the single-spin left-right asymmetries. We compare
the results with the available data and make predictions for future
experiments.Comment: submitted to Phys. Rev .

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